Direct Digitisation for Position Measurement of Charged Particle Beams: Sampling and Quantisation Effects on Resolution

With the technology improvements of Analog-to-Digital Converters (ADC), notable in terms of sampling rate and achievable resolution, the direct digitisation of beam pickup signals is of growing interest in the field of particle beam diagnostics for charged particle accelerators. This thesis studies the possibility to acquire and measure the transverse position of a charged particle beam circulating in an accelerator, using an architecture based on minimum analogue signal conditioning of the Beam Position Monitor (BPM) electrodes signals, direct digital conversion, and measurement of the power of each beam bunch-related pulse signal in the digital domain. The aim is to analyse the impact of the characteristics of the sampling stage on the system resolution performance. The effects of the distortion due to the sampling process, and of the finite resolution of the ADC, are discussed analytically in detail. The results are expressed in form of a general, analytic expression of the expected signal-to-noise ratio of the measurement for any pulse waveform as function of the characteristics of the analog-to-digital converter. The presented model was applied to analyse the performance of the Large Hadron Collider beam extraction interlock BPM system, an example of system implementing direct-digitisation of BPM signals. A prototype setup was used to acquire beam data with two different ADCs, one with higher sampling rate, the other with higher resolution. The system was also replicated in a parametric simulation framework and the estimated performance from analytical prediction, simulation, and measurements are compared. The analytic model of the effects of digitisation proves to be a valid tool to understand and quantify how the sampling stage limits the measurement resolution and how the choice of the ADC can be optimised.